[EM] Juho: Seat% and vote%--What I mean by "unattainable".

[Michael Ossipoff]

Juho:

Seat% and Vote%:

I don't just mean that it's generally impossible to make all the
parties' seat% equal to their vote%.  Of course that's impossible. But
I mean more than that.

I mean that it's also in general, with fixed house-size, impossible to
even put every party's seat% as close as possible to its vote%.

In general, no method can do that. Not SL, and not LR.

As I said, putting every party's seat% as close as possible to its
vote% amounts to putting every party's number of seats as close as
possible to its number of Hare quotas.

Of course that's generally impossible with fixed house-size.

But, if you want to put each party's seat% _as close as possible_ to
its vote%, than that means you want to put each party's number of
votes as close as possible to its number of Hare quotas.

And that desire (generally unattainable with fixed house-size), on
your part, was the premise of an argument that I've posted here a few
times in recent days. An argument whose conclusion was that what you
say you want undeniably leads to your wanting what Sainte-Lague does.
I won't repeat that argument here, but it's in several recent posts,
over the past few days.

Equal representation and s/q argument:

But there is one argument of mine that I'd like to repeat in this
post. I'm repeating it because it's so simple and brief. And because
you have either missed it, or tried to evade it. If the latter, then
I'm now making you have to evade it twice. Of course refusal to answer
would be a perfectly good evasion method, and I won't criticize you
for it.

You said that you agree that people have a right to equal
representation for everyone (too the extent achievable).

Equal representation for everyone means equal representation for each
person. Equal representation for each person means an equal number of
seats for each person. An equal number of seats for each person means
equal s/q
(where q is a unit of population or vote).

Therefore, you agree that people have a right to equal s/q, to the
extent achievable.

If you disagree with one or more of the statements in the two
paragraphs before this one, then don't hesitate to say which
statement(s) you disagree with, and why.

Advantage of LR:

As I've said, LR's value is as a contingency-plan for if splitting
strategy were a problem in SL, and remained even if the 1st SL
denominator were raised from 1 to 2.

In other words, if people are abusing rounding-off to the nearest
integer,  and if the problem can't be avoided, then abandon rounding
off, and, instead just round up the parties with the largest
remainder (fractional part of a Hare quota).

You'd be substituting, for rounding-off, a sort of horse-race that
gives the next seat to the party with the largest fractional part of a
Hare quota.

Why is the Hare quota the best divisor for that method?

Because there are as many Hare quotas are there seats. That means that
it's always possible, by rounding some parties up and some down, to
give a number of seats equal to the desired house-size.

Mike Ossipoff